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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
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A L G F B R A. C ap. XXXI.
leat Objectionem Facere: inveniet, Ei idem paulo acencius perpendai candem Eibi
ipsi lacistacere. Nam ipsa valoris a ambisuitas in aequationibus simplicibus, id
iplum cst quod aequationem composicam tacit esse anibiguam, es duarum Radi-
cum capacem. Ineicatque, haec Mulciplicario, modum conticiendi s quationem.
cujus Radix ita Sic ambigua.
Duod partim Patebre ex ipsa substitutione duarum a e pro ambiguo ralore ipsi
uS a. Nam, PFOPIeE a = B, AEUE a C = B C Le mutuo destrUanE; itemique -Ca
=bc: adeoque totum nihilo XquetUT. Ee Similiter, PrOPtEF C =C, FC uE a C = c a
se mutuo destruant; itemque = be-BC: unde iterum totum aquetur nibilo. LF
quidem, proprer cum a ==b, tum e = c, Fit ut quatuor membra a C, b e, C a, bc,
ejuldem sine vatoris omnia: quorum cum duo aftirmentur, et duo negentur, se
mutuo perimunt omnia, tiuntque nihilo aequalia.
Acque hoc in anibisua Aquatione Ouadratica necessario fieri, manifectum cst.
Cum enim, propter a = b, (uc jam ostentum est) ac - be semucuo destruant;
id pariter Het s utrobique PrO C POnAtIEa hoC CA a a = ba; (quod complet
aequationem quadraticam a a = b a = ca f bc =- 0, pro valore ipliris a = b.
Trerumque, cum propter e =0, etiam ac - c a se mucuo destruant; idem tiet li
utrobique pro an Ponatur e; hoc clt e0 = cc: (quod complet aequationem qua-
draticam ee -b e cc f b0 ==0; pro valore ip(uS e = c.) Constabit itaque
Duadratica A quatio secundum utrumris ralorem.
Lciam porro manitestum exit, (pariter constare quadraticam illam aequationem,
Tumpto per toram uroris ralore iptius a auc c:) Tubstituro ubique vel b velc,
DTO a aUT C.
Ouippe in hac aequatione
Si pro a substituatur B, Het
Si pro a Cubsticuatur c, tiet
aa = ba - ca + bc =0.
bb - bb - cb = b6 =0.
c6 - b0 - 66 + b5 = 0.
Adeoque, utroris modo, termini se muuo destruune. Inde constac; urovis Tum.
Dio ralore radieis an quadraticam illam aequationem recte contictere.
Idem pariter constabit, si utcunque rarientur (quos jam potuimus astirmativos
ambos) ralores illi amibisuxe radicis a: Pura, li lic alcer alturmacirus, alter ne-
sacirus, aue eriam uterque negatirus. Nam posito
= = b, ec a = - c. Quibus inter se mulciplicatis ha-
betur aequario Ouadratica,
aa ba + Ca b6 - 0.
Potitoque, proa, ubique f b, tet bb- bb +6b- b6= 0.
Et Polico, proa, ubique - c, tiet c0+ b6- 66 - bc-=0.
Terminis, urrovis modo, se manifeste destruentibus.
Similiter; Fi a =
b, e
a = -c. Ouippe cum tce,
mulciplicando,
aa t ba LCa f bc- .
EF, DOtO - B, lOa II bb bb- cb + b0-0
Politoque = 6, PrO an Fiet C6 - b0 - c5 + bc--0.
Terminis etiamnum se mutuo destruentibus. Onde liquet ucrumvis ralorem a
bisux radicis a, indisterenter lumi posle.
Idemque pariter conspicietur, in quibulris Aquationibus compoliis, quoteun-
que ractieum; sumpro per totam, pro ambigua radice, quoris ejus ralore. Vnon
Ec mecuendum; ne nobis imponat hic proceltus.
-b-
tca B6-0.
C